Pour the red wine into a large saucepan and bring to a gentle boil. Reduce by half until slightly syrupy.
Preheat your oven to 140°C (275°F). Pat the ribs dry, season well, dredge lightly in seasoned flour. Heat oil in a heavy, ovenproof pot and sear ribs on all sides until deeply browned. Remove and set aside.
Tip off excess fat, leaving about 1 tbsp in the pan. Add shallots first — cook over medium heat until lightly caramelised. Then add carrots, celery, leek, and garlic. Cook until golden brown, scraping up any fond from the bottom. Stir in tomato paste and cook for 2 minutes, stirring constantly.
Add the reduced wine to deglaze the pan, scraping the base clean. Return the short ribs (and any juices) to the pot. Pour over the beef stock — enough to almost cover the ribs. Add bay leaves and thyme.
Transfer to the oven and braise for 3½–4 hours, until tender and falling off the bone. Let the ribs cool in the liquid for 30–45 minutes before removing them gently. Strain the braising liquid through a fine sieve — discard the veg.
Simmer the strained liquid until slightly thickened and glossy. Whisk in mustard and a splash of vinegar.
Make the celeriac purée: Simmer the celeriac and potatoes in milk with a pinch of salt until soft. Blend with a knob of butter until smooth and glossy.
